# Asymptotic estimation of the convergence of solutions of the equation $\dot{x}\left(t\right)=b\left(t\right)x(t-\tau \left(t\right))$

Archivum Mathematicum (2001)

- Volume: 037, Issue: 4, page 279-287
- ISSN: 0044-8753

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topDiblík, Josef, and Khusainov, Denis. "Asymptotic estimation of the convergence of solutions of the equation $\dot{x}(t)=b(t) x(t-\tau (t))$." Archivum Mathematicum 037.4 (2001): 279-287. <http://eudml.org/doc/248755>.

@article{Diblík2001,

abstract = {The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot\{x\}(t)=b(t)x(t-\tau (t))$. Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x(t)$ reaches an $\varepsilon $ - neighbourhood of origin and remains in it.},

author = {Diblík, Josef, Khusainov, Denis},

journal = {Archivum Mathematicum},

keywords = {stability of trivial solution; estimation of convergence of nontrivial solutions; stability of trivial solution; estimation of convergence of nontrivial solutions},

language = {eng},

number = {4},

pages = {279-287},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Asymptotic estimation of the convergence of solutions of the equation $\dot\{x\}(t)=b(t) x(t-\tau (t))$},

url = {http://eudml.org/doc/248755},

volume = {037},

year = {2001},

}

TY - JOUR

AU - Diblík, Josef

AU - Khusainov, Denis

TI - Asymptotic estimation of the convergence of solutions of the equation $\dot{x}(t)=b(t) x(t-\tau (t))$

JO - Archivum Mathematicum

PY - 2001

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 037

IS - 4

SP - 279

EP - 287

AB - The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x}(t)=b(t)x(t-\tau (t))$. Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x(t)$ reaches an $\varepsilon $ - neighbourhood of origin and remains in it.

LA - eng

KW - stability of trivial solution; estimation of convergence of nontrivial solutions; stability of trivial solution; estimation of convergence of nontrivial solutions

UR - http://eudml.org/doc/248755

ER -

## References

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